Question

Given that f(x)=x, g(x)=x-1: h(x)=sqrtx-1.
find f0g0h.

Answer 1

As posted, h(x) is interpreted as sqrtx-1 = sqrt(x)-1. If h(x) is meant to be sqrt(x-1), you only have to make appropriate changes to get the right answer. In general, be sure to include all required parentheses in posts.
f(x)=x
g(x)=x-1
h(x)=sqrt(x)-1
Since composition of functions is associative, i.e.
f ° (g ° h) = (f ° g) ° h,
the order of composition is not important.
(f°g°h)(x)
= f°(g(h(x)))
=f(g(h(x)))
=f(g(sqrt(x)-1))
=f(sqrt(x)-1 -1)
=sqrt(x)-2